{
  "id": 2314,
  "curve_key": "39957005544289:-231787485594067373713",
  "ainvs": [
    "1",
    "0",
    "0",
    "-832437615506",
    "268272483401110020"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 93.95647539171578,
  "faltings_height": 5.793781780005408,
  "conductor": "180681270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "43",
    "107"
  ],
  "discriminant": "5826626086734714191474163527870054400",
  "regulator": "5.551254814441785412130494842702542278895",
  "points": [
    [
      "392728",
      "43661086"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=32; A=(3q-p)(p+q)^3=990927, B=-(p+3q)(p-q)^3=6758095. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 19:53:52",
  "updated_at": "2026-09-26 19:53:52"
}